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Chapter 2: Problem 15

Translate to an inequality. Normandale Community College is no more than 15 mi away.

Short Answer

Expert verified
\( d \leq 15 \)

Step by step solution

01

- Understand the problem

Identify the key information in the statement: Normandale Community College is no more than 15 miles away. This means the distance is less than or equal to 15 miles.
02

- Identify the variable

Let the variable represent the unknown distance. For example, let d represent the distance from the starting point to Normandale Community College.
03

- Write the inequality

Since the distance is no more than 15 miles, we write this as the variable 'd' being less than or equal to 15. The inequality is: \( d \leq 15 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

translating word problems
When dealing with word problems in algebra, the first step is always to understand the problem. Carefully read the statement and identify the key information. In our example, the statement is: 'Normandale Community College is no more than 15 miles away.'
Here are a few strategies to help:
  • Identify keywords: Words like 'no more than' can be translated to 'less than or equal to' in algebraic terms.
  • Determine what you are trying to find: In this problem, we need to determine the distance to Normandale Community College.
  • Choose a variable: Selecting a variable, like 'd' for distance, can simplify the translation process.
By focusing on these steps, you can easily translate word problems into algebraic expressions or inequalities.
distance inequality
An inequality is a mathematical statement that shows the relationship between two expressions that are not necessarily equal. In our problem, the distance from a starting point to Normandale Community College should not exceed 15 miles.
This means the distance 'd' can be either equal to or less than 15 miles. We express this using an inequality: \( d \leq 15 \)
This type of inequality is crucial in representing real-world problems. It allows us to model limitations and constraints effectively.
  • Symbol '\(' \leq \)' means 'less than or equal to'.
  • This symbol can be used when the maximum value is given.
  • Remember, the distance can be exactly 15 miles or anything less.
Understanding and using distance inequalities can help you solve a variety of problems involving limits, boundaries, and measurements.
algebraic expressions
An algebraic expression represents mathematical relationships using variables, numbers, and operations. In our word problem, we need to express the distance in algebraic terms to solve it.
Here are the steps to form the expression:
  • Select a variable: We choose 'd' to represent the distance.
  • Translate the problem: The phrase 'no more than 15 miles' becomes 'd is less than or equal to 15'.
  • Write the expression: This translates to the inequality \( d \leq 15 \).
By using variables and forming expressions, algebra allows us to generalize problems and find solutions efficiently.
Always break down the word problem into smaller parts. Then, focus on how these parts interact using algebraic expressions and inequalities.

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Most popular questions from this chapter

Solve using the addition and multiplication principles. $$ \frac{3}{4}\left(3 x-\frac{1}{2}\right)-\frac{2}{3}<\frac{1}{3} $$

How is the use of statistics in each of the following misleading? a) A business explaining new restrictions on sick leave cited a recent survey indicating that \(40 \%\) of all sick days were taken on Monday or Friday. b) An advertisement urging summer installation of a security system quoted FBI statistics stating that over \(26 \%\) of home burglaries occur between Memorial Day and Labor Day.

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Use an inequality and the five-step process to solve each problem. Most insurance companies will replace a vehicle if an estimated repair exceeds \(80 \%\) of the "blue-book" value of the vehicle. Michelle's insurance company paid \(\$ 8500\) for repairs to her Subaru after an accident. What can be concluded about the blue-book value of the car?
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